Fourier Optics: An Introduction

E.G. Steward

In Fourier Optics E.G. Steward surveys the application to optics of
Fourier transforms and associated principles. It offers some rigour but
is written in such a way that it can be read rather than worked through.
Diagrams and a few halftones are used to good effect, good motivation
is provided, with key concepts approached through basic applications,
and aspects of the history of optics are touched on. There are also a
few exercises at the end of each chapter, with solutions provided.

Steward begins with basic concepts such as spatial and temporal coherence,
diffraction and aperture, and so forth. He then works through Fraunhofer
diffraction for single and double slits, circular apertures, n-slit
gratings, and crystals. Chapter three introduces Fourier series and
periodic structures and chapter four Fourier transforms, convolution,
and correlation — all explained by application to optical systems.

Chapter five applies all of this to optical imaging, both incoherent and
coherent, and touches on holography and optical processing. Chapter six
looks at applications to medical imaging: the focus is on X-ray computed
tomography, but short contributions by other authors cover MRI and
ultrasonic computed tomography. And chapter seven looks at the study
of radiation sources and astronomical applications: Michelson's stellar
and spectral interferometers, partial coherence, Fourier transform
spectroscopy, aperture synthesis, and the intensity interferometer.

There's not enough room in two hundred pages to go into the details of
any of these topics, but enough is presented to give a broad idea of
what is involved. Fourier transforms, phasor diagrams, basic optics
and so forth are explained as required, or treated in appendices, but
in a manner more suited as a refresher for someone who has done courses
covering those topics than for a complete beginner. Fourier Optics
has an obvious niche as a higher undergraduate text or an easy graduate
text — or, in my case, as an accessible survey for someone with a maths
and physics background who's recently taken up photography and wants to
understand modulation transfer functions and other aspects of optics.